Preheat oven to 350°F. Line cookie sheets with parchment or silicone baking mats.
Whisk baking soda, salt, and flour in a medium bowl. Set aside.
Cream butter and sugars in the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer). Cream until fluffy, about 1 minute.
Add egg and vanilla and mix until combined. Slowly mix in dry ingredients, scraping the sides of the bowl as necessary.
Scoop 1 tablespoon cookie balls onto the cookie sheets, 2” apart.
Bake for 7-8 minutes, until the edges are golden. Remove from the oven and tap the cookie sheets on the top of the stove lightly to flatten the cookies a bit. Let cool completely before frosting.
To make the frosting: mix butter with a hand mixer until creamy and smooth. Mix in powdered sugar slowly until crumbly. Add coconut extract and 1 tablespoon milk and mix until smooth. Add up to 1 more tablespoon of milk to get the right spreading consistency for your frosting, but only add 1 teaspoon or less at a time so you don't make it too runny. Stir in coconut.
Frost the bottoms of half the cookies, then sandwich with another cookie. Store in an airtight container for up to 4 days.